2025 TJC Promo Q4

2025 TJC Promo Q4

Junior College 1
9 marks
  1. Find \(\displaystyle \int \frac{1}{x^2+px-2p^2}\,dx\), where \(p\) is a constant.[3]
  2. Find \(\displaystyle \int \frac{1+x}{\sqrt{1-2x^2}}\,dx\).[3]
  3. Using integration by parts, find \(\displaystyle \int \tan^{-1}2x\,dx\).[3]

Solution:

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Answer:\(\dfrac1{3p}\ln\left|\dfrac{x-p}{x+2p}\right|+C\); \(\dfrac1{\sqrt2}\sin^{-1}(\sqrt2x)-\dfrac12\sqrt{1-2x^2}+C\); \(x\tan^{-1}(2x)-\dfrac14\ln(1+4x^2)+C\)

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